Find an equation of a plane that passes through the points P(4,2,1), Q(-1,-2,2), R(3,1,-2) a. 13x-16y+4z=24 b. -11x+y-10z=33 c. 3x+15y+4z=21 d. -4x-5y+2k=-7

Q: Find the equation of the plane passing through the points (1,0, -1), (-1,2,1) and parallel to the…

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Q: Find an equation of the plane containing the point (3,0,-4) and perpendicular to the line r(t)=…

A: A detailed solution is given below

Q: find an equation for the plane through pointsP, Q, and R. P(1, -1, 2), Q(2, 1, 3), R(-1, 2, -1)

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Q: Which of the following is the equation of the plane where x-2y + 32 = 3 and x+y+z=2 and passes from…

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Q: Determine the equation of the plane passing through the points P(–2, 1, 5) and Q(4, 9,-3) and…

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Q: Find an equation of the plane through the point (2, 0, 1) and perpendicular to the line x = 3t, y =…

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Q: Find an equation of the plane that passes through the points M(1,2,3), N(-3,-2,5), and 0(2,-3,4).

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: Find the equation of the plane that passes through the points 4 = (2,4,-3), B = (3,-1,3) and y - 4 -…

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Q: Find an equation of the plane determined by the points P(0,0,0), Q(-1,2,4), and R(2,1,3)

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Q: Find the equation of the plane passing through (0,0,-4)and perpendicular to the line joining the…

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Q: Find the equation of the plane through the point P = (2, 5, 4) and parallel to the plane 5x – 5y +…

A: Equation of plane parallel to 5x -5y +3z = 6  is given by; 5x -5y +3z + λ  = 6 Also it passes…

Q: Write the equation of the plane that contains the point P(1, 3, 5) and the line L: x = 4t, y = 6 +…

A: It can be solved using properties of plane.

Q: Find an equation of the plane. the plane that passes through (8, 0, -1) and contains the line x = 5…

A: The equation of plane through a point and contains a line

Q: Find the equation of the plane through the point (2, –1, –5) and containing the line | x = 3 – 2t, y…

A: We have to find the equation of the plane, passing through the point (2,-1,-5) and containing the…

Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

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Q: Q7) The equation of the plane contains the points (3,2,1), (2,1,-1) and (-1,3,2) is 2x-9y-5z=16. * F

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2)…

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Q: Write the equation for the plane through the points P(-1, -7, 45), Q(2, 3, -6) and R(1, -4, 33).…

A: Here we have to find the equation of the plane through the points P(-1,-7,45),Q(2,3,-6) and…

Q: Find the intersection of the line r(t) = (2, 1, 3) + t(3, -3, 1) and the plane 4x - 4y - 2z = 6.

A: Given, Line-> r(t) = (2, 1, 3) + t(3, -3, 1) Plane-> 4x - 4y - 2z = 6 ------equation 1

Q: Find an equation of the plane that passes through the points P, Q, and R. Р(5, —3, 4), Q(3, -5, —6),…

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Q: Find an equation of the plane containing the point P(1, -2, -2) perpendicular to the line through…

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Q: Determine the equation of the plane through the points (1, 0, 3) and the line l : ¯r = (3, 4, 1) +…

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2, –2)…

A: The equation of the plane passing through the points (x0 , y0 , z0) and perpendicular to a vector…

Q: Find an equation for the plane that passes through the point (1, 3, -5) and is perpendicular to the…

A: Given point is (1,3,-5). The scalar equation of a plane that passes through point (a, b, c) and has…

Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: Find the equation of the plane that contains the line 2 5-x 2+y – 5 – z, and the 3 point P( 0,5,2).…

A: We have to find the equation of the plane that contains the line and the point.

Q: Find an equation for the plane that passes through the following points. (2, –1, 4), (0, 0, 6), and…

A: Explanation of the solution is given below...

Q: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

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Q: Find the point at which the line (-4, 1,1) + t(2, -5, 4) intersects the plane -5x+ 3y – 3z = -54.

A: the given line is  xyz=-411+t2-54 xyz=-411+2t-5t4t xyz=-4+2t1-5t1+4t

Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

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Q: Find the equation of a plane passing through points (3,2,2), (1,0,-1) and parallel to the line…

A: Equation of plane is calculated as below:

Q: 5. Find the equation of the plane that passes through the point (6,0,-2) and contains the line X =…

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Q: Find the point at which the line (-3, -4,-2)+t(5, -4,-2) intersects the plane -5x +3y+z= -155.

A: Given: line equation: -3,-4,-2 +t (5,-4,-2) Then equation of line from parametric equation is given…

Q: Determine the general form of the equation of the plane passing through P(2,1,-1), Q(0,-2,0) and…

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Q: Find the equation of the plane passing through the points A(2,2,1), B(9,3,6) and perpendicular to…

A: Here we have to find the equation of the plane passing through the points A(2,2,1) ,B(9,3,6) and…

Q: Write the equation for the plane through the point P(- 4,4,2) and perpendicular to the line x =4+7t,…

A: Explanation of the answer is as follows

Q: Find an equation of the plane that is parallel to the plane x+ 2y – 10z + 12 = 0 and contains the…

A: The equation of the given plane is  x+2y-10z+12=0 We need to find the equation of plane that is…

Q: Find the equation of the plane through the point (1,4,7) and perpendicular to the line x = 2 + t, y…

A: If the plane is perpendicular to the line, then the line is also perpendicular to the plane.  So the…

Q: Write the equation for the plane through the points P(-1, 1,-12), Q(2, 8, -49) and R(1, -6, 45). 4x…

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Q: what is the equation of the plane perpendicular to the intersection line of the x-2y+2z= 3  and…

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Q: Find an equation of the plane that passes through the points P, Q, and R. P(3, -5), e(6, 3, -3),…

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Q: Find the equation of a plane that contains the lines and - 2+5. O A 2x-y-22 = 42 O B. 2x y 2z -10 O…

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Q: Find the equation of the plane passing throught (0,0,-4) and perpendicular to the line joining the…

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Q: Find an equation of the plane. The plane that passes through the point (2, 4, 5) and contains the…

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Q: Find the equation of the plane passing through the points O = (0, 0,0), A = (1, -2, –5) and B =…

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Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

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Q: Which of the following planes is the equation for the plane with an x-intercept at P(2,0,0), a…

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